In single-particle entanglement (SPE) two degrees of freedom a single particle are entangled. SPE is resource that can be exploited both in quantum communication protocols and experimental tests noncontextuality based on the Kochen-Specker theorem. certified via test contextuality Bell inequalities. Experiments Bell-type inequality violation by entangled systems may affected an analog locality ...

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...

We use the Lagrange inversion theorem to characterize the central coefficients of matrices in the Bell subgroup of the Riordan group of matrices. We give examples of how by using different means of calculating these coefficients we can deduce the generating functions of interesting sequences.

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...

Bell inequalities play a central rôle in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality whic...

Two new formulations of Bell’s theorem are given here. First, we consider a definite set of two entangled photons with only two polarization directions, for which Bell’s locality assumption is violated for the case of perfect correlation. Then, using a different approach, we prove an efficient Bell-type inequality which is violated by some quantum mechanical predictions, independent of the effi...

We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also cons...

We present a simple model demonstrating that time-symmetric (advanced + retarded) relativistic interactions can account for statistical correlations violating the Bell inequalities while avoiding conspiracies as well as the commitment to instantaneous (direct space-like) influences. We provide an explicit statistical analysis of the model while highlighting some of the difficulties arising from...